Preheat oven to 400°.
Heat oil in a large nonstick skillet over medium-high heat. Add carrot; sauté 2 minutes or until tender. Add garlic; sauté 15 seconds. Add 1/4 teaspoon salt and spinach; sauté 2 minutes or until spinach wilts.
Combine 1/4 teaspoon salt, green onions, and next 4 ingredients (through grated ginger).
Fold 4 (16 x 12-inch) sheets heavy-duty foil in half lengthwise. Open foil; place about 1/2 cup spinach in center of each foil sheet. Top each with 1 fillet. Drizzle mirin mixture evenly over fillets; sprinkle evenly with black pepper. Fold foil over fillets; tightly seal edges. Place foil packets in a single layer on a jelly-roll pan. Bake at 400° for 20 minutes or until fish flakes easily when tested with a fork. Serve with lime wedges.